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Madison Industries <br />Designed by: ML/JFB <br />August 4, 2016 <br />Job No: WCA17860-1 <br />Customer: Mobil Fueling Canopy <br />Structure: 65'-0" x 54'-4" (4) Column Canopy <br />Location: Tracy, CA 95377 <br />Sheet 14 <br />Roof Support Beam B1, cont. <br />Factored Service Load Moments: <br />Bottom flanges cantilever & span in compression: <br />Case 1: Full DL + LL over entire beam -- Checks critical negative bending in span & cantilever <br />Mu, (cant) = Mu, (span) = max{[(Wu2)a2/2 + (P1u20)],[(Wu2)b2/2 -+' (P2u2)(b)]} = 43.5 ft -k <br />Top flange span in compression: <br />Case 2: Full DL + LL over span; DL only on cantilever -- Checks crit. pos. bending stress in span <br />Case 2A: Actual loads x'= 13.00 ft <br />Mu'(span) _[Rlcase2(ract)-(0.9P1pL+0.9WpLa)](x')/2 - [2(0.9P1oL)+0.9WpLa](a)/2 = 26.2 ft -k <br />Case 213: For roof members <br />Is this a roof member? (y/n) y <br />Mul(span) = (Wut)(L2)/8 + P'L/4 = 26.5 ft -k <br />Where P'= (1.4)(200 lbs) if tributary area < 200 ft2 or <br />(1.4)(2000 lbs) for larger tributary areas <br />Factored moment for design of span top flange = Mu'(span) = 26.5 ft -k <br />Bottom flange span & top flange cantilever in compression: <br />Case 3: Full DL + WIND UPLIFT over entire length -- Checks crit. neg. bending stress in span <br />& crit. pos. bending stress in cantilever <br />Case 3A: Span <br />Case 36: Cantilever <br />Factored service load design moments: <br />Top flange span in compression: <br />Bottom flange span in compression: <br />Top flange cantilever in compression: <br />Bottom flange cantilever in compression <br />Unbraced Length Limits: <br />LP = 300ry/sgrt(F,) = <br />L, = ryXt/FL(1+sgrt(1+X2FL2))1i2 = <br />mull (span) = (Wu3)(L2)/8 = <br />Mu'(cant) = (Wu3)(a2)/2 + max[P1u3a,P2u3b] = <br />Mu (span) = <br />Mull (span) = <br />Mu (cant) = <br />Mull (cant) = <br />3.68 ft <br />9.68 ft <br />Where: Xt = (n/SX)(EGJA/2)1/2 = 1612 <br />X2 = (4C,/ly)(S,/GJ)2 = 0.027 <br />FL = (Fy- 10) = 40 ksi <br />26.5 ft -k <br />43.5 ft -k <br />20.2 ft -k <br />43.5 ft -k <br />15.4 ft -k <br />20.2 ft -k <br />JUN 6$ 2017 <br />T <br />